Let the temperature (as a function of time) be T = a sin (nt + b) where t is the time in hours.
Set t = 0 as 4 AM and find the values of a, n and b.
Substitute the temperature values into the LHS of the equation and solve for t in each case.
In a particle accelerator, a fast moving particle (with v = 0.99c) decays into two photons, of total energy of 6.2 × 10−27 J. What is the rest mass of the fast moving particle?
there's a way to do it without using a substitution: use the fact that a = eln(a)
i.e. 2 = eln(2)
So 2ln(x) = eln(x)*ln(2)
then integrate the RHS to get the answer
Prove by induction that n(n + 1)(n + 2) is divisible by 6
When n = 1, n(n + 1)(n + 2) = 6, which obviously works
Assume true for n = k, i.e. k(k + 1)(k + 2) = 6M
Consider n = k + 1
(k + 1)(k + 2)(k + 3) = 6M/k (k + 3) <--- how do i prove this is divisible by 6?
You can start by finding the sum of consecutive odd integers:
1 + 3 + 5 + ... + (2n - 1)
Sn = n/2 (2a + (n-1)d) = n/2 (2x1 + (n - 1)x2) = n/2 (2 + 2n - 2) = n * n = n2
But this is not always divisible by 4